MCQ
If a, m, n are positive ingegers, then $\big\{\sqrt[\text{m}]{\sqrt[\text{n}]{\text{a}}}\big\}^{\text{mn}}$ is equal to
- A$\text{a}^\text{nm}$
- ✓$\text{a}$
- C$\text{a}^{\frac{\text{m}}{\text{n}}}$
- D$1$
✓
Answer
Correct option: B.
$\text{a}$
Find the value of $\big\{\sqrt[\text{m}]{\sqrt[\text{n}]{\text{a}}}\big\}^{\text{mn}}.$
So,
$\big\{\sqrt[\text{m}]{\sqrt[\text{n}]{\text{a}}}\big\}^{\text{mn}}=\bigg\{\sqrt[\text{m}]{\text{a}^{\frac{1}{\text{n}}}}\bigg\}^{\text{mn}}$
$=\bigg\{\text{a}^{\frac{1}{\text{n}}\times\frac{1}{\text{m}}}\bigg\}^{\text{mn}}$
$=\bigg\{\text{a}^{\frac{1}{\text{n}}\times\frac{1}{\text{m}}}\times\text{m}\times\text{n}\bigg\}$
$\Rightarrow\big\{\sqrt[\text{m}]{\sqrt[\text{n}]{\text{a}}}\big\}=\bigg\{\text{a}^{\frac{1}{\text{n}}\times\frac{1}{\text{m}}}\times\text{m}\times\text{n}\bigg\}$
$\Rightarrow\big\{\sqrt[\text{m}]{\sqrt[\text{n}]{\text{a}}}\big\}=\text{a}$
Hence the correct choice is $b$.
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